Search

We introduce a group naturally acting on aperiodic necklaces of length n with two colors using a one-to-one correspondence between such necklaces and irreducible polynomials of degree n over the field F2 of two elements. We notice that this group is isomorphic to the quotient group of nondegenerate circulant matrices of size n over that field modulo a natural cyclic subgroup. Our groups turn out to be isomorphic to the sandpile groups for a special sequence of directed graphs. Bibliography: 15 titles., UDC 515.16 1. INTRODUCTION This work originated in the research of the first author related to the Drinfeld associator (6). It is well known (e.g., see (5)) that the logarithm [...]

We construct four geometries E1,…,E4 with the diagramsuch that any two elements of type 1 are incident to at most one common element of type 2 and three elements of type 1 are pairwise incident to common elements of type 2 if and only if they are incident to a common element of type 5. The automorphism group Ei of Ei is flag-transitive, isomorphic to 2E6(2) : 2, 3·2E6(2) : 2, 226 : F4(2) and E6(2) : 2, for i=1,2,3 and 4. We calculate the suborbit diagram of the collinearity graph of Ei with respect to the action of Ei. By considering the elements in Ei fixed by a subgroup Ti of order 3 in Ei we obtain four geometries T1,…,T4 with the diagramon which CEi(Ti) induces flag-transitive action, isomorphic to U6(2) : 2, 3·U6(2) : 2, 214 : Sp6(2) and L6(2) : 2 for i=1,2,3 and 4. Next, by considering the elements fixed by a subgroup Si of order 7 in Ei we obtain four geometries with the diagramon which CEi(Si) induces flag-transitive action isomorphic to L3(4) : 2, 3·L3(4) : 2, 28 : L3(2) and (L3(2) × L3(2)) : 2, for i=1,2,3 and 4. [Copyright &y& Elsevier]

Examines how the stability number can be computed as the solution of a conic linear program over the cone of copositive matrices. Equations for conic programming of convex cones; Analysis of stability via copositive programming; Approximation of copositive cone.